Promising to press investigations into what went wrong, congressional Republicans on Sunday said that Health and Human Services Secretary Kathleen Sebelius should leave over the website problems that have crippled the rollout of the Affordable Care Act.

“If she cannot reorganize to get the kind of team in consistently to meet his agenda, then she shouldn’t be there,” said Issa, speaking on CBS’ "Face the Nation."

To congressional Republicans battered by public disapproval of their government-shutdown strategy, the bungled design of the program’s website is providing an opportunity to resume the offensive against the Obama administration and the ambitious health insurance expansion known as Obamacare.

The website that was supposed to be the main entryway for users, Healthcare.gov, has been plagued with long delays and troubling errors in transmitting data to insurance companies. President Obama named Jeffey Zients, deputy budget director, to supervise an overhaul; Zients has pledged that the site will be working well by the end of November.

Issa said Sunday he would press for why the website was changed to require users to create an account before they could check the prices on the insurance exchanges. In a letter to the administration last week, Issa charged that the problems stemmed from a “political decision,” so users wouldn’t get upset about prices. Democrats have said Issa is twisting the facts.

Sebelius is set to testify Wednesday before the House Energy and Commerce Committee. Rep. Marsha Blackburn (R-Tenn.), vice chairman of that committee, said Sunday that she wants to know how much money has been spent already, and how much it will take to get it working correctly.

“We want her to talk with us before she is out the door,” Blackburn said on "Fox News Sunday." “But I tell you, the incompetence in building this website is staggering.”

Sen. John Barrasso (R-Wyo.), mentioning a “Saturday Night Live” skit that had Sebelius' mock advice to citizens trying to navigate the website, said on ABC’s “This Week” that Sebelius was “the laughingstock of America.”

But last week Sebelius was defiant: “The majority of people calling for me to resign, I would say, are people who I don't work for and who do not want this program to work in the first place.”

“I’m a taxpayer, she works for me, she’s a public servant,” said Rep. John Fleming (R-La.), who has called for her resignation. Speaking on CNN’s “State of the Union,” he said Sebelius is “obviously not taking accountability for this.”

In his weekly address, Obama on Saturday repeated that the website would be fixed but also took a swipe back at his Republican critics’ expressions of concern, “considering they’ve spent the last few years so obsessed with denying those same people access to health insurance that they just shut down the government and threatened default over it.”

Democrats, while also expressing disappointment in the rollout, said the Republican hunt for a scapegoat was just a distraction from the job of getting the website working.

“I think she should stay, and I think she will get the job done,” said Sen. Joe Manchin (D-W.Va.), on “This Week.” Manchin has called for a one-year delay in the part of the law that imposes a tax penalty on people who don’t sign up for health insurance.

Kentucky Gov. Steve Beshear, a Democrat, said his state-run exchange has been successful so far and promises to be a turning point in healthcare for his state, which he says consistently has some of the poorest health statistics in the country. He said on NBC’s “Meet the Press” that news media and critics should “take a deep breath.”

“Look, this is going to take some time to get done, but everybody needs to chill out because it is going to work,” he said.